If $m \angle QPS = 180^\circ$ and $m \angle RPS = 123^\circ$, what is $m \angle QPR$, in degrees? $123^\circ$ $P$ $Q$ $S$ $R$
Solution: From the diagram, we see that $\angle QPR$ and $\angle RPS$ are supplementary angles. Therefore, $m \angle QPR + m \angle RPS = 180^\circ$ Thus, $m \angle QPR = 180^\circ - m \angle RPS = 180^\circ - 123^\circ = 57^\circ$.